The relationship between the secondary mathematics curriculum, college persistence, and success at an urban community college

According to Venezia, Kirst, and Antonio (2003) and Barth’s 2002 Thinking K16 Ticket to Nowhere report, the disconnect between K-12 and postsecondary education was a contributing factor to high attrition rates. Since mathematics emerged as a primary concern for college readiness, Barth (2002) called for improving student transitions from K-12 to postsecondary institutions through the use of state or local data. The purpose of the present study was to analyze mathematics course-taking patterns of secondary students in a local context and to evaluate high school characteristics in order to explore their relationships with Associate degree attainment or continuous enrollment at an urban community college. Also, this study extended a national study conducted by Clifford Adelman (The Toolbox Revisited, 2006) as it specifically focused on community college students that were not included his study. Furthermore, this study used the theoretical framework that human capital, social capital, and cultural capital influence habitus—an individual’s or a group’s learned inclination to behave within the parameters of the imposed prevailing culture and norms. Specifically, the school embedded culture as it relates to tracking worked as a reproduction tool of ultimate benefit for the privileged group (Oakes, 1994). ^ Using multilevel analysis, this ex post facto study examined non-causal relationships between math course-taking patterns and college persistence of public high school graduates who enrolled at the local community college for up to 6 years. One school-level variable (percent of racial/ethnic minorities) and 7 student-level variables (community college math proportion, remedial math attempts, race, gender, first-year credits earned, socioeconomic status, and summer credits earned) emerged as predictors for college persistence. Study results indicated that students who enter higher education at the community college may have had lower opportunities to learn and therefore needed higher levels of remediation, which was shown to detract students from degree completion. Community college leaders are called to partner with local high schools with high percentages of racial/ethnic minorities to design academic programs aimed at improving the academic preparation of high school students in mathematics and promote student engagement during the first year and summers of college. ^

Grade A Taipei junior high school principals’ self-reported leadership practices

The principal’s leadership and curriculum development are considered the core elements for creating a high performing junior high school. In Taiwan, mathematics curriculum reform has been an ongoing topic since 1994. The pedagogy, classroom interactions, and the underlying philosophy of mathematics education have varied with different versions of guidelines. These changes inevitably increase the requirement for principals’ leadership in order to effectively implement the curriculum reform. Principals’ leadership is essential to the success of the implementation in their school. This study aimed to explore and identify the leadership of junior high school principals whose schools had been judged by the Taipei City Government as Grade A junior high schools. Principals’ implementations of the reformed mathematics curriculum were used as examples to generate insights of their leadership. This study drew upon a multiple-case study approach. Data were collected from interviews, observations, and documentations. Bass and Avolio’s (1997) full range leadership theory provided a structure for gaining insight into these principals’ leadership practices. Five Grade A Taipei junior high school principals participated and shared their leadership concepts and experiences. Findings revealed that the leadership preferences of the five principles varied considerably. Management by exception-active, contingent reward, individualised consideration, and idealised influence were Grade A Taipei junior high school principals’ preferred leadership practices. In addition, principals’ leadership strategies associated with these practices were identified. These principals had adopted a range of leadership strategies according to the staff and school needs. Results of this study have implications for both Taiwanese principals and education departments. Principals can enhance their leadership by gaining more understanding about the Grade A principals’ leadership practices and strategies. Taiwanese education departments can improve school leadership training programs by focusing on these practices and strategies, which may also lead to more effective strategies for implementing national curriculum reform.

A cross-national study of calculus

The results from a cross-national study comparing calculus performance of students at East China Normal University (ECNU) in Shanghai and students at the University of Michigan before and after their first university calculus course are presented. Overall, ECNU significantly outperformed Michigan on both the pre- and post-tests, but the Michigan students showed a larger gain and normalized gain, and hence narrowed the gap. ECNU's superior performance was especially striking on the subset of problems requiring only a pre-calculus background. On those, Michigan's post-test scores were below ECNU's pre-test scores and, indeed, ECNU's higher performance on both the overall pre-test and overall post-test is attributable to its success on these problems.

Politics, Power, PISA: a genealogy of mathematics education policy at second level in Ireland at the beginning of the 21st century

This thesis traces a genealogy of the discourse of mathematics education reform in Ireland at the beginning of the twenty first century at a time when the hegemonic political discourse is that of neoliberalism. It draws on the work of Michel Foucault to identify the network of power relations involved in the development of a single case of curriculum reform – in this case Project Maths. It identifies the construction of an apparatus within the fields of politics, economics and education, the elements of which include institutions like the OECD and the Government, the bureaucracy, expert groups and special interest groups, the media, the school, the State, state assessment and international assessment. Five major themes in educational reform emerge from the analysis: the arrival of neoliberal governance in Ireland; the triumph of human capital theory as the hegemonic educational philosophy here; the dominant role of OECD/PISA and its values in the mathematics education discourse in Ireland; the fetishisation of western scientific knowledge and knowledge as commodity; and the formation of a new kind of subjectivity, namely the subjectivity of the young person as a form of human-capital-to-be. In particular, it provides a critical analysis of the influence of OECD/PISA on the development of mathematics education policy here – especially on Project Maths curriculum, assessment and pedagogy. It unpacks the arguments in favour of curriculum change and lays bare their ideological foundations. This discourse contextualises educational change as occurring within a rapidly changing economic environment where the concept of the State’s economic aspirations and developments in science, technology and communications are reshaping both the focus of business and the demands being put on education. Within this discourse, education is to be repurposed and its consequences measured against the paradigm of the Knowledge Economy – usually characterised as the inevitable or necessary future of a carefully defined present.

Analyzing Australian middle years students' preferred mathematics classroom practices

The Middle Years of schooling have become an issue for mathematics teachers and educators, and calls for the reform of this period of schooling are frequent. However, the suggested reforms appear to be divided in their views of what would be best for these students. This paper provides a brief overview of what some Middle Years students say about their needs. Some 1500 students in the Middle Years of schooling (Years 5 to 9) were surveyed about their preferred mathematics classroom activities: the methods and results of the survey may be extremely relevant to those contemplating Middle Years reform.

Using everyday experiences in teaching secondary mathematics in Malawi : possibilities and constraints for change

Proponents of socially and culturally oriented mathematics education have argued that teaching approaches which value and connect with the learner's prior knowledge and everyday experience are more likely to promote active, meaningful, relevant and liberatory learning than approaches which rely on transmission and abstract presentation of mathematical content. In Malawi, proposals to reform the outdated secondary mathematics curriculum have been made with the aim of aligning mathematics instruction with the social and political changes in the current Malawian society. Using a case study approach, this study investigated the extent to which everyday experiences could be used as a vehicle for changing the learning and teaching of secondary mathematics in Malawi. The study was collaborative, taking place over a period of five months in severely overcrowded and poorly resourced classes in two schools. It involved three mathematics teachers in a cycle of planning and teaching mathematics lessons based on the use of everyday experiences, and observation of and reflection on these lessons, in order to document the effects of using everyday experiences on student learning and teachers' teaching practices. The data was collected through student questionnaires; classroom observations and fieldnotes; interviews and reflective meetings with teachers; and informal meetings with key education officials in Malawi. Mathematics examination results from students involved in this study and a corresponding group from the previous year were collected. A reflective and critical approach was adopted in the interpretation and discussion of the data. Teachers' participation in this study resulted in heightened awareness of their teaching roles and the value of linking school mathematics with everyday experience. The study also shows that students found mathematics interesting and important to learn despite their lack of success in it. In addition, the study documented a number of constraints to change in mathematics instruction such as teachers' focus on mathematics content and examination requirements, and students' resistance to inquiry learning. It also recorded possibilities and barriers to collaboration both between teachers and researchers, and teachers themselves. The findings of this study are timely since they could serve to inform the reform of the Malawian secondary mathematics curriculum currently being undertaken, which began without a critical examination of the classroom conditions necessary to accommodate a socio-politically relevant mathematics education.

Teaching secondary school mathematics : research and practice for the 21st century

For the last decade or so, educational policy makers and researchers in many countries have been calling for significant changes to the way mathematics is taught in secondary schools. Australian mathematics curriculum documents now promote learning goals that go beyond mastery of a pre-determined body of knowledge and procedures - the traditional emphasis on facts, skills, formulae - to include mathematical reasoning and problem solving, communication, and real world applications. There is also pressure to move away from over-reliance on teacher-centred practices such as exposition and individual seatwork, towards activities that promote learners' involvement in constructing, applying, and evaluating mathematical ideas. Further impetus for reform comes from research recommending that if learners are to develop mathematically powerful forms of thinking and habits of mind, then classrooms should immerse them in the authentic practices of the discipline by supporting a culture of collaboration and sense-making. Teaching Secondary School Mathematics - incorporates recent developments in research and practice and applications to teaching mathematics in Australian secondary schools. Covering such areas as curriculum, pedagogy and assessment; teaching mathematical content; equity and diversity in the classroom; and professional and community engagement, it is an invaluable resource for all practising and pre-service mathematics teachers.

Embedding university perspectives in university teaching and learning : lessons learnt and possibilities for reforming/decolonising curriculum

Embedding Indigenous knowledge in the curriculum continues to challenge traditional western perspectives on Indigenous epistemologies and cultures. This paper will initially discuss experiences of embedding Indigenous perspectives in the curriculum at an Australian university. The project was inspired by the Reconciliation Statement which ensured funding through Teaching and Learning Large Grants. Its successful outcomes included the creation of identified positions for Indigenous academics within faculties, creation of a resource hub of relevant teaching materials and consistent documentation and awareness of Indigenous perspectives through interviews and workshops. The paper concludes by critically interrogating the methodology used to conceptualise Indigenous knowledge in embedding Indigenous perspectives in a university curriculum. This paper argues for a thorough curriculum reform if a degree of decolonisation of the western constructed Indigenous knowledge and its living systems are desired.

Future directions and perspectives for problem solving research and curriculum development

Since the 1960s, numerous studies on problem solving have revealed the complexity of the domain and the difficulty in translating research findings into practice. The literature suggests that the impact of problem solving research on the mathematics curriculum has been limited. Furthermore, our accumulation of knowledge on the teaching of problem solving is lagging. In this first discussion paper we initially present a sketch of 50 years of research on mathematical problem solving. We then consider some factors that have held back problem solving research over the past decades and offer some directions for how we might advance the field. We stress the urgent need to take into account the nature of problem solving in various arenas of today’s world and to accordingly modernize our perspectives on the teaching and learning of problem solving and of mathematical content through problem solving. Substantive theory development is also long overdue—we show how new perspectives on the development of problem solving expertise can contribute to theory development in guiding the design of worthwhile learning activities. In particular, we explore a models and modeling perspective as an alternative to existing views on problem solving.

Civics and citizenship education in the national history curriculum : conducting the same music or rehearsing an incomplete tune?

This paper raises some questions about teaching and teacher education in the social sciences in response to the decision to implement a national curriculum in Australia. In particular, it contends that the decision to focus on discipline-specific knowledge in the social sciences will not necessarily meet the hopes of the Melbourne Declaration and deliver a 21st century curriculum that prepares students for the future. In doing so, it suggests that social educators need to engage with the broader discourse and political context shaping the push for curriculum reform in Australia and makes reference to the marginalisation of civics and citizenship education in the latest draft of the Australian curriculum: History.

Mentors report on their own mentoring practices

There are only two ways to implement reform in an education system, namely through inservice education of existing teachers and preservice teacher education. Implementing the Australian Curriculum will require targeting both teachers and preservice teachers. Classroom teachers in their roles as mentors have a significant role to play for developing preservice teachers. What mentors do in their mentoring practices and what mentors think about mentoring will impact on the mentoring processes and ultimately reform outcomes. What are mentors’ reports on their mentoring of preservice teachers in science and mathematics? This mixed-method study presents mentors’ reports on their mentoring of primary preservice teachers (mentees) in mathematics (n=43) and science (n=29). Drawing upon a previously validated instrument (Hudson, 2007), this instrument was amended to allow mentors to report on their perceptions of their mentoring. A questionnaire elicited extended written responses that focused on: (1) the mentors’ rapport with their mentees, (2) successful mentoring strategies, (3) aspects that may lead the mentee to feel unsuccessful, and (4) ways to enhance their mentoring skills. Mentors claimed they mentored teaching mathematics more than science. However, 20% or more indicated they did not provide mentoring practices for 25 out of 34 survey items in the science and 9 out of 34 items in the mathematics. Educational reform will necessity mentors to be educated on effective mentoring practices so the mentoring process can be more purposeful. Indeed, mentors who have knowledge of such practices may address the potential issues of more than 20% of mentees not receiving these practices. These mentors also claimed that professional development on effective mentoring can enhance their skills. To ensure the greatest success for an Australian Curriculum will require targeting mentors for professional development in order to assist mentees’ development into the profession.

Comparing mentors’ reports on their own mentoring of primary preservice teachers

Implementing the Australian Curriculum will require targeting both teachers and preservice teachers as enactors of reform. Classroom teachers in their roles as mentors have a significant role to play for developing preservice teachers. What mentors do in their mentoring practices and what mentors think about mentoring will impact on the mentoring processes and ultimately reform outcomes. What are mentors’ reports on their mentoring of preservice teachers for teaching science and mathematics? This quantitative study presents mentors’ reports on their mentoring of primary preservice teachers (mentees) in mathematics (n=43) and science (n=29). Drawing upon a previously validated instrument (Hudson, 2007), this instrument was amended to allow mentors to report on their perceptions of their mentoring. Mentors claimed they mentored teaching mathematics more than science. However, 20% or more indicated they did not provide mentoring practices for 25 out of 34 survey items in the science and 9 out of 34 items in the mathematics. Educational reform will necessity mentors to be educated on effective mentoring practices for mathematics and science so the mentoring process can be more purposeful. Indeed, mentors who have knowledge of such practices may address the potential issues of more than 20% of mentees not receiving these practices. To ensure the greatest success for an Australian Curriculum mentors may need professional development in order to assist mentees’ development into the profession.

Students' perceptions of the relevance of mathematics in engineering

In this paper, we report on the findings of an exploratory study into the experience of students as they learn first year engineering mathematics. Here we define engineering as the application of mathematics and sciences to the building and design of projects for the use of society (Kirschenman and Brenner 2010)d. Qualitative and quantitative data on students' views of the relevance of their mathematics study to their engineering studies and future careers in engineering was collected. The students described using a range of mathematics techniques (mathematics skills developed, mathematics concepts applied to engineering and skills developed relevant for engineering) for various usages (as a subject of study, a tool for other subjects or a tool for real world problems). We found a number of themes relating to the design of mathematics engineering curriculum emerged from the data. These included the relevance of mathematics within different engineering majors, the relevance of mathematics to future studies, the relevance of learning mathematical rigour, and the effectiveness of problem solving tasks in conveying the relevance of mathematics more effectively than other forms of assessment. We make recommendations for the design of engineering mathematics curriculum based on our findings.

External management of curriculum change

At a time of rapid curriculum reform, some schools are turning to external change agents for assistance, but what's the best way to initiate such an approach?

Principals’ and teacher leaders’ perceptions of their role and interaction under current Chinese reform : a case study in Shandong province

This study aims to explore the perceptions of principals and teacher leaders regarding their roles and the interaction between these roles in Chinese urban primary schools at the time of unprecedented curriculum reform. This involves a complexity of factors such as the influence of globalisation, the impact of traditional Chinese cultural attitudes towards education through Confucianism, and the implementation requirements of the current education reforms. All of these wider contextual factors help to shape the leadership practices that are described in the study. A qualitative exploratory case study approach has been utilised to undertake this investigation. The conceptual framework for this study draws upon scholars‘ work from Western countries but has been adapted in order to address three research questions for the study‘s focus on the context in Shandong province, Mainland China. Three research questions were addressed: First, what are principals‘ perceptions of their leadership roles in Mainland China under current educational reform? Second, what are teacher leaders‘ perceptions of their leadership roles in Mainland China under current educational reform? And finally, what are principals‘ and teacher leaders‘ perceptions of how their roles interact? With reference to the principals in the study, the findings confirm Gurr‘s (2008) comprehensive leadership model relating to four roles, specifically, learning and teaching, symbolic and cultural awareness, future orientation, and accountability. Significantly, some sub-roles that emerge from the data are uniquely Chinese. For example, school culture construction is a very deliberate process in which principals and their staff talked openly about and were involved in creating a positive school climate comprising spiritual, material, and system dimensions. Another finding relates to school feature construction. This refers to the process that principals and staff used to make their schools distinctive and different from other schools and included such features as the school‘s philosophy and the school-based curriculum. In seeking to understand the nature of teacher leadership in Chinese primary schools, this research confirms some findings identified in Western literature. For instance, teacher leaders in Shandong province were involved in decision-making, working with parents and community members, undertaking and planning professional development for staff, and mediating between colleagues (Day & Harris, 2002; Harrison & Killion, 2007; Leithwood, Jantzi, & Steinbach, 1999; Muijs & Harris, 2006; Smylie, 1992). However, some new aspects, such as a heightened awareness of the importance of accountability, emerge from this study. The study‘s conceptual framework also draws upon some significant insights from micropolitics and, in particular, two core constructs, namely cooperation and conflict (Blase, 1991), to explore the interactions between principals and teacher leaders. In this study, principals and teacher leaders employed exchange and facilitation as two strategies in cooperative processes; and they adopted enforcement and compromise in conflictive processes. Finally, the study‘s findings indicate that principals and teacher leaders were developing new ways of interacting in response to the requirements of significant education reform. Most principals were exercising their power through (Blase, 1991) their teacher leaders who in turn, were working in alignment with their principals to achieve the desired outcomes in schools. It was significant that this form of 'parallel leadership' (Crowther, Ferguson, & Ham, 2009) characterised the teacher leadership roles at this period of change to the curriculum in Mainland China.